I'm not particular about the thickness of patch, but my rifle sure is. There was a wear-in period for both my GPRs (the other is a 54). They both started out with really tight bores and enough sharp edges to cut patches and make starting balls pretty tough with real tight patch/ball combos. I'll stick with talking about the 50, but it mirrors what happened in the 54, as well as what my hunting pard experienced with his.
I had to start out with .490 balls and .015 commercial pre-lubed patches because the .018 pillow ticking I had on hand was really hard to get going and shredded miserably. I was disappointed because the ticking and my own lube are lots cheaper than commercial patches for a guy that shoots lot.
But after a couple of hundred rounds fired, it was getting really easy to start the .015/.490 combo. Out of curiosity I tried my ticking and homemade lube, and shazam. No more cut patches and a jump in accuracy.
Lymans just come with really sharp rifling right up to the muzzle and crown, and it seems to take some firing to smooth out the sharp. Not a prob, but something to plan for.
Also put some brake pad cleaner on a few cleaning patches and scrub the heck out of the new bore. Lyman uses some kind of bore grease that is the dickens to get out any other way, yet really affects accuracy till you get it out. Brake cleaner does it easily with 3 or 4 patches.
As for why Pyrodex P rather than RS? It's just more accurate and less fouling in m GPR 50. Same for my GPR 54, as a matter of fact. I've still got about 15 cans of RS and Select I picked up free from a friend's estate. And believe me, I'd be using the free stuff rather than buying P if it worked anywhere close to the P.
And you didn't ask, but I'll harp on the cheap side. I know you'll want to be using the commercial products at first just cuzz it's easier while you're figuring out what's going on. But don't let it be a habit if you want to shoot lots.
I bought my pillow ticking from Walmart. Can't remember the exact price but it was less than $5 for enough for roughly 1000 patches. My lube is tallow from a deer I shot mixed with a little olive oil. Call it 10 cents worth of olive oil for about 2 years worth of lube. I spent $20 on a Lee .490 RB mould and I shoot free scrap lead. If I threw the mould away after casting only 1000 balls (not a chance, but this is a mental game), I'd still have only about $25 in 1000 balls, 1000 patches and more lube than I needed. Figure the mold as a lifetime investment, then I've got only $5/1000 in my patch/ball/lube setup.
Like I said. Cheap. You can't even buy 1000 pellets for an air rifle for $5.